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Properties

Label 495.6.k
Level $495$
Weight $6$
Character orbit 495.k
Rep. character $\chi_{495}(208,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $296$
Sturm bound $432$

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Defining parameters

Level: \( N \) \(=\) \( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 495.k (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 55 \)
Character field: \(\Q(i)\)
Sturm bound: \(432\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(495, [\chi])\).

Total New Old
Modular forms 736 304 432
Cusp forms 704 296 408
Eisenstein series 32 8 24

Trace form

\( 296 q - 40 q^{5} + O(q^{10}) \) \( 296 q - 40 q^{5} + 404 q^{11} - 71952 q^{16} - 984 q^{20} - 1976 q^{22} - 8102 q^{23} + 3962 q^{25} + 5968 q^{26} - 9688 q^{31} - 30830 q^{37} + 70136 q^{38} + 47532 q^{47} - 69608 q^{53} - 65650 q^{55} + 96936 q^{56} - 53656 q^{58} + 86390 q^{67} + 176400 q^{70} - 164452 q^{71} - 71424 q^{77} - 144472 q^{80} - 420680 q^{82} + 771168 q^{86} + 285160 q^{88} - 336768 q^{91} - 366168 q^{92} + 977158 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(495, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{6}^{\mathrm{old}}(495, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(495, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 2}\)